Question 1

Given the line $8x - 17 = 6y + 7$, what is the slope of the line?

Question 2

What is the $y$-intercept of the line $8x - 17 = 6y + 7$?

Accepted Answer

$(0, 4)$

Question 3

The endpoints of a diameter of a circle are $(5,6)$ and $(-1,2)$. What is the equation of the circle?

Accepted Answer

$(x-2)^2 + (y-4)^2 = 13$

Question 4

Given $f(x) = 6 - 2|x-4|$, what is the vertex of the graph of $f(x)$?

Accepted Answer

$(4, 6)$

Question 5

If $f(x) = 3x - 2$ and $g(x) = x^2 + x$, what is $(f \circ g)(2)$?

Accepted Answer

$16$

Question 6

If $f(x) = 3x - 2$ and $g(x) = x^2 + x$, what is $(g \circ f)(2)$?

Accepted Answer

$20$

Question 7

Solve for $x$: $\log_3(7-x) + \log_3(2x+1) = 3$.

Accepted Answer

$x = 5/2$

Question 8

What is the domain of $f(x) = \frac{x^2-9}{x-3}$?

Accepted Answer

$x 
eq 3$

Question 9

What is the domain of $f(x) = \frac{5x-11}{18-x}$?

Accepted Answer

$x 
eq 18$

Question 10

Which of the following is the correct formula for the distance $d$ between points $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

Question 11

Given $f(x) = 6 - 2|x-4|$, what is the range of $f(x)$?

Accepted Answer

$[0, 6]$

Question 12

If $f(x) = 3x - 2$ and $g(x) = x^2 + x$, what is $f(g(x))$?

Accepted Answer

$3x^2 + 3x - 2$

Question 13

If $f(x) = 3x - 2$ and $g(x) = x^2 + x$, what is $g(f(x))$?

Accepted Answer

$9x^2 - 12x + 2$

Question 14

Which of the following is the correct equation for a circle with center $(h, k)$ and radius $r$?

Accepted Answer

$(x-h)^2 + (y-k)^2 = r^2$

Question 15

Given the function $f(x) = \frac{x^2-9}{x-3}$, what is the value of $f(4)$?

Accepted Answer

$7$

Question 16

If $f(x) = 6 - 2|x-4|$, for which value of $x$ does $f(x) = 0$?

Accepted Answer

$x = 7$ or $x = 1$

Question 17

Which of the following is NOT in the domain of $f(x) = \frac{5x-11}{18-x}$?

Accepted Answer

$x = 18$

Question 18

If $\log_3(7-x) + \log_3(2x+1) = 3$, which of the following is a valid solution?

Accepted Answer

$x = 5/2$

Question 19

Given the endpoints of a diameter of a circle at $(5,6)$ and $(-1,2)$, what is the center of the circle?

Accepted Answer

$(2,4)$

Question 20

Given $f(x) = 6 - 2|x-4|$, what is the $x$-intercept(s) of the graph?

Accepted Answer

$x = 7$ and $x = 1$

Precalculus Exam 1 Preparation: Key Concepts and Problem Types

Study Guide - Practice Questions